We found the Forest Covertype in the UCI Machine Learning Repository that takes forestry data from the Roosevelt National Forest in northern Colorado (Click here for a tour of the area). The observations are taken from 30m by 30m patches of forest that are classified as one of seven forest types:

  1. Spruce/Fir
  2. Lodgepole Pine
  3. Ponderosa Pine
  4. Cottonwood/Willow
  5. Aspen
  6. Douglas-fir
  7. Krummholz


The actual forest cover type for a given observation (30 x 30 meter cell) was determined from US Forest Service (USFS) Region 2 Resource Information System (RIS) data. The data

Kaggle hosted the dataset in a competition with a training set of 15,120 observations and a test set of 565,892 observations. The relative sizes of the training and test sets makes classification of cover type a challenging problem.

Data Exploration

Name Measurement Description
Elevation meters Elevation in meters
Aspect azimuth Aspect in degrees azimuth
Slope degrees Slope in degrees
Horizontal Distance To Hydrology meters Horz Dist to nearest surface water features
Vertical Distance To Hydrology meters Vert Dist to nearest surface water features
Horizontal Distance To Roadways meters Horz Dist to nearest roadway
Hillshade 9am 0 to 255 index Hillshade index at 9am, summer solstice
Hillshade Noon 0 to 255 index Hillshade index at noon, summer soltice
Hillshade 3pm 0 to 255 index Hillshade index at 3pm, summer solstice
Horizontal Distance To Fire Points meters Horz Dist to nearest wildfire ignition points
Wilderness Area (4 binary columns) 0 (absence) or 1 (presence) Wilderness area designation
Soil Type (40 binary columns) 0 (absence) or 1 (presence) Soil Type designation
Cover Type (7 types) 1 to 7 Forest Cover Type designation - Dependent Variable

Some class seperation is clearly visible in the following plots of elevation.

Another compelling variable is aspect, or the cardinal direction that the slope has the steepest gradient downwards. For example, in the rose diagram below, there are more Douglas-Fir trees for observations with northern aspects (near 0º) than southern aspects (near 180º).

One of the more interesting facets of the dataset was the distribution of Hillshade luminance. Hillshade is measured on a scale from 0 to 255 (dark to bright)

Hillshade at time t varies as a factor of \[\cos(slope)\cos (90- Altitude) + \sin (slope)\sin (90-Altitude)\cos(Azimuth-Aspect)\]

where Altitude is the angle of the Sun relative to the horizon and Azimuth relates to the direction the Sun is facing:North , South , East or West. Azimuth of 90 degrees corresponds to East.

This equation actually arises from a theorem in Spherical geometry known as “Spherical law of Cosines” relating the sides and angles of triangles constructed on spherical surfaces.

https://upload.wikimedia.org/wikipedia/commons/3/38/Law-of-haversines.svg

In a unit sphere, lengths a,b,c correspond to the angle subtended by those sides from the center of the sphere. If we know the two sides a,b and the angle between them C, then the cosine of c, is given by

In short, the Illumination of the patch is related to alitude of the sun, slope of the terrain and the relative direction of the sun and the slope.

\[Hillshade(t_1,t_2,t_3)\] has has been plotted below in 3 dimensions

More importantly, in the context of class seperation , The following plot of Elevation, Slope and Hillshade clearly seperates the forest cover types showing that Elevation could be the most significant factor in determining cover type.

The primary reason for the collection of cartographic data pertains to terrain mapping and is ultimately useful for applying topographic correction to satellite images in remote sensing or as background information in scientific studies.

Topographic correction is necessary if,for example we wish to identify materials on the Earth’s surface by deriving empirical spectral signatures, or compare images taken at different times with different Sun and satellite positions and angles. By applying the corrections it is possible to transform the satellite-derived reflectance into their true reflectivity or radiance in horizontal conditions.

References:

https://en.wikipedia.org/wiki/Spherical_law_of_cosines https://scientiaplusconscientia.wordpress.com/2014/12/16/hillshading-useful-fun-with-digital-elevation-models/ https://scientiaplusconscientia.wordpress.com/2014/08/06/working-with-modis-l1b-from-scratch-4-topographic-and-illumination-correction/ http://www.geography.hunter.cuny.edu/~jochen/GTECH361/lectures/lecture11/concepts/Hillshade.htm